PA28 is quite different to C152 in the feel, things are in a different place (eg trim is right down between the seats) but you shouldn't struggle. Very dosile stall, nice approach with full flap, and just about a 4 seater if you compromise on fuel.
If you bash every instructor who says set 2200 and don't lean, i think there would be a shortage overnight. For a PA28, 2300 rpm leaned is about 75% power for 2-3000' where you will spend most of your time, so instructors generally don't bother pointing out the actual % power you are using.
As for leaning, clubs are generally paranoid about overleaning with high power settings and the damage this can cause. Sure, it's fine to lean at any level but you won't see any massive benefit below 5-6000'.
You don't officially need any training if you have an SEP rating, so differences training is a bit misleading, but most clubs will require a checkout before you fly a new type and you'd be a bit stupid to just go off and fly a completely different aircraft unless you are fairly experienced.
As for locking the POH away, this is completely inexcusable. I can see why you were perhaps told to come in at 75kts. At big commercial airports you can get away with it, i've know people only use 2 flap and keep the speed up to prevent holding up commercial traffic on the ILS, or to fit more landings into a circuit session, but as soon as you apply that to somewhere with a shorter runway you're in trouble.